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ImportantConcepts06 - Physics 136 Kip Thorne Important...

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Physics 136 Caltech Kip Thorne Nov 10, 2002 Important Concepts Chapters 1 through 6 I Frameworks for physical laws and their relationships to each other A General Relativity, Special Relativity and Newtonian Physics: Sec. 1.1 B Phase space for a collection of particles: Chap 2 C Phase space for an ensemble of systems: Chap 3 D Relationship of Classical Theory to Quantum Theory 1 Mean occupation number as classical distribution function: Sec. 2.3 2 Mean occupation number determines whether particles behave like a classical wave, like classical particles, or quantum mechanically: Secs. 2.3 & 2.4; Ex. 2.1; Fig. 2.5 3 Geometric optics of a classical wave is particle mechanics of the wave's quanta: Sec. 6.3 4 Geometric optics limit of Schrodinger equation is classical particle mechanics: Ex. 6.6 II Physics as Geometry A Newtonian: coordinate invariance of physical laws 1 Idea Introduced: Sec. 1.2 2 Newtonian particle kinetics as an example: Sec. 1.4 B Special relativistic: frame-invariance of physical laws 1 Idea introduced: Sec. 1.2 2 Relativistic particle kinetics: Sec. 1.4 3 4-momentum conservation: Secs. 1.4 & 1.12 a Stress-energy tensor: Sec. 1.12 4 Electromagnetic theory: Sec. 1.10 a Lorentz force law: Sec. 1.4 5 Kinetic theory: Chap. 2 a Derivation of equations for macroscopic quantities as integrals over momentum space [Sec. 2.5] b Distribution function is frame-invariant and constant along fiducial trajectories [Secs. 2.2 & 2.7] C Statistical mechanics: invariance of the laws under canonical transformations (change of generalized coordinates and momenta in phase space): Sec. 3.2, Ex. 3.1 III
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